结构性能概率模型的小样本建模方法

Small samples method to establishment for the probability characteristic of structural performance

目前通过试验建立结构性能概率模型的过程中,一般采用经典统计学中的矩法推断其中关键的计算模式不定性系数的概率特性,并以此为基础推断结构性能的概率特性;但样本容量不足时,矩法的推断结果会受到显著的统计不定性的影响,存在较大的因过高估计结构性能而导致额外失效风险的可能.针对目前试件数量(样本容量)普遍不足的现象,利用贝叶斯法提出建立结构性能概率模型的小样本方法,与矩法、区间估计法、一般贝叶斯法的对比分析结果说明:在统计不定性的反映程度、推断结果的等效置信水平和推断结果本身等方面,文中贝叶斯法都具有较好的表现,推断结果稳妥、适中,且便于应用,可作为小样本条件下建立结构性能概率模型的一个基本方法.

At present,in the process of establishing the structural performance probability model through the structural test,the probability characteristic of key model uncertainty coefficient is inferred from the moment method in classical statistics.On the basis of this,one can infer the probability characteristic of structural performance.However,a limited number of samples will cause uncertainties in the estimations of statistical parameters using the moment method and overestimate the structural performance,which will lead to additional failure risk of structures.Aimed at the insufficiency of sample numbers,the paper proposes the small samples method to establish the probability characteristic of structural performance using the Bayesian method.According to comparative analysis among the moment,the interval estimation methods and the Bayesian method,it shows that the proposed Bayesian method not only does well in reflecting statistical uncertainty,ensuring the confidence level of inference result and the inference result itself,but also its inference result is more accurate and convenient to put it into use,which can be used as a basic method to establish the structural performance probability model under the condition of small samples.